Method and apparatus of operating a scanning probe microscope

ABSTRACT

An improved mode of AFM imaging (Peak Force Tapping (PFT) Mode) uses force as the feedback variable to reduce tip-sample interaction forces while maintaining scan speeds achievable by all existing AFM operating modes. Sample imaging and mechanical property mapping are achieved with improved resolution and high sample throughput, with the mode workable across varying environments, including gaseous, fluidic and vacuum.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. Non-Provisional patentapplication Ser. No. 15/137,937, filed Apr. 25, 2016 (and issued as U.S.Pat. No. 9,588,136 on Mar. 7, 2017), which is a continuation of U.S.Non-Provisional patent application Ser. No. 14/288,180, filed May 27,2014 (and issued as U.S. Pat. No. 9,322,842 on Apr. 26, 2016), which isa continuation of U.S. Non-Provisional patent application Ser. No.12/618,641, filed Nov. 13, 2009 (and issued as U.S. Pat. No. 8,739,309on May 27, 2014), which claims priority under 35 U.S.C. § 119(e) to U.S.Provisional Patent Application No. 61/114,399, filed on Nov. 13, 2008,the entirety of each of which is expressly incorporated by referenceherein.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention is directed to scanning probe microscopes (SPMs),including atomic force microscopes (AFMs), and more particularly, to amode of AFM operation that provides force control at high speed, lowtip-sample interaction forces and high resolution.

Description of Related Art

Scanning probe microscopes (SPMs), such as the atomic force microscope(AFM), are devices which typically employ a probe having a tip and whichcause the tip to interact with the surface of a sample with low forcesto characterize the surface down to atomic dimensions. Generally, theprobe is introduced to a surface of a sample to detect changes in thecharacteristics of a sample. By providing relative scanning movementbetween the tip and the sample, surface characteristic data can beacquired over a particular region of the sample, and a corresponding mapof the sample can be generated.

A typical AFM system is shown schematically in FIG. 1. An AFM 10 employsa probe device 12 including a probe 17 having a cantilever 15. A scanner24 generates relative motion between the probe 17 and a sample 22 whilethe probe-sample interaction is measured. In this way, images or othermeasurements of the sample can be obtained. Scanner 24 is typicallycomprised of one or more actuators that usually generate motion in threemutually orthogonal directions (XYZ). Often, scanner 24 is a singleintegrated unit that includes one or more actuators to move either thesample or the probe in all three axes, for example, a piezoelectric tubeactuator. Alternatively, the scanner may be a conceptual or physicalcombination of multiple separate actuators. Some AFMs separate thescanner into multiple components, for example an XY actuator that movesthe sample and a separate Z-actuator that moves the probe. Theinstrument is thus capable of creating relative motion between the probeand the sample while measuring the topography or some other property ofthe sample as described, e.g., in Hansma et al. U.S. Pat. No. RE 34,489;Elings et al. U.S. Pat. No. 5,266,801; and Elings et al. U.S. Pat. No.5,412,980.

Notably, scanner 24 often comprises a piezoelectric stack (oftenreferred to herein as a “piezo stack”) or piezoelectric tube that isused to generate relative motion between the measuring probe and thesample surface. A piezo stack is a device that moves in one or moredirections based on voltages applied to electrodes disposed on thestack. Piezo stacks are often used in combination with mechanicalflexures that serve to guide, constrain, and/or amplify the motion ofthe piezo stacks. Additionally, flexures are used to increase thestiffness of actuator in one or more axis, as described in applicationSer. No. 11/687,304, filed Mar. 16, 2007, entitled “Fast-Scanning SPMScanner and Method of Operating Same.” Actuators may be coupled to theprobe, the sample, or both. Most typically, an actuator assembly isprovided in the form of an XY-actuator that drives the probe or samplein a horizontal, or XY-plane and a Z-actuator that moves the probe orsample in a vertical or Z-direction.

In a common configuration, probe 17 is often coupled to an oscillatingactuator or drive 16 that is used to drive probe 17 to oscillate at ornear a resonant frequency of cantilever 15. Alternative arrangementsmeasure the deflection, torsion, or other characteristic of cantilever15. Probe 17 is often a microfabricated cantilever with an integratedtip 17.

Commonly, an electronic signal is applied from an AC signal source 18under control of an SPM controller 20 to cause actuator 16 (oralternatively scanner 24) to drive the probe 17 to oscillate. Theprobe-sample interaction is typically controlled via feedback bycontroller 20. Notably, the actuator 16 may be coupled to the scanner 24and probe 17 but may be formed integrally with the cantilever 15 ofprobe 17 as part of a self-actuated cantilever/probe.

Often, a selected probe 17 is oscillated and brought into contact withsample 22 as sample characteristics are monitored by detecting changesin one or more characteristics of the oscillation of probe 17, asdescribed above. In this regard, a deflection detection apparatus 25 istypically employed to direct a beam towards the backside of probe 17,the beam then being reflected towards a detector 26, such as a fourquadrant photodetector. The deflection detector is often an opticallever system such as described in Hansma et al. U.S. Pat. No. RE 34,489,but may be some other deflection detector such as strain gauges,capacitance sensors, etc. The sensing light source of apparatus 25 istypically a laser, often a visible or infrared laser diode. The sensinglight beam can also be generated by other light sources, for example aHe—Ne or other laser source, a superluminescent diode (SLD), an LED, anoptical fiber, or any other light source that can be focused to a smallspot. As the beam translates across detector 26, appropriate signals areprocessed by a signal processing block 28 (e.g., to determine the RMSdeflection of probe 17). The interaction signal (e.g., deflection) isthen transmitted to controller 20, which processes the signals todetermine changes in the oscillation of probe 17. In general, controller20 determines an error at Block 30, then generates control signals(e.g., using a PI gain control Block 32) to maintain a relativelyconstant interaction between the tip and sample (or deflection of thelever 15), typically to maintain a setpoint characteristic of theoscillation of probe 17. The control signals are typically amplified bya high voltage amplifier 34 prior to, for example, driving scanner 24.For example, controller 20 is often used to maintain the oscillationamplitude at a setpoint value, A_(S), to insure a generally constantforce between the tip and sample. Alternatively, a setpoint phase orfrequency may be used. Controller 20 is also referred to generally asfeedback where the control effort is to maintain a constant target valuedefined by setpoint.

A workstation 40 is also provided, in the controller 20 and/or in aseparate controller or system of connected or stand-alone controllers,that receives the collected data from the controller and manipulates thedata obtained during scanning to perform data manipulation operationssuch as point selection, curve fitting, and distance determiningoperations. The workstation can store the resulting information inmemory, use it for additional calculations, and/or display it on asuitable monitor, and/or transmit it to another computer or device bywire or wirelessly. The memory may comprise any computer readable datastorage medium, examples including but not limited to a computer RAM,hard disk, network storage, a flash drive, or a CD ROM.

AFMs may be designed to operate in a variety of modes, including contactmode and oscillating mode. Operation is accomplished by moving thesample and/or the probe assembly up and down relatively perpendicular tothe surface of the sample in response to a deflection of the cantileverof the probe assembly as it is scanned across the surface. Scanningtypically occurs in an “x-y” plane that is at least generally parallelto the surface of the sample, and the vertical movement occurs in the“z” direction that is perpendicular to the x-y plane. Note that manysamples have roughness, curvature and tilt that deviate from a flatplane, hence the use of the term “generally parallel.” In this way, thedata associated with this vertical motion can be stored and then used toconstruct an image of the sample surface corresponding to the samplecharacteristic being measured, e.g., surface topography. In onepractical mode of AFM operation, known as TappingMode™ AFM (TappingMode™is a trademark of the present assignee), the tip is oscillated at ornear a resonant frequency of the associated cantilever of the probe, orharmonic thereof. A feedback loop attempts to keep the amplitude of thisoscillation constant to minimize the “tracking force,” i.e., the forceresulting from tip/sample interaction, typically by controllingtip-sample separation. Alternative feedback arrangements keep the phaseor oscillation frequency constant. As in contact mode, these feedbacksignals are then collected, stored and used as data to characterize thesample.

Regardless of their mode of operation, AFMs can obtain resolution downto the atomic level on a wide variety of insulating or conductivesurfaces in air, liquid or vacuum by using piezoelectric scanners,optical lever deflection detectors, and very small cantileversfabricated using photolithographic techniques. Because of theirresolution and versatility, AFMs are important measurement devices inmany diverse fields ranging from semiconductor manufacturing tobiological research. Note that “SPM” and the acronyms for the specifictypes of SPMs, may be used herein to refer to either the microscopeapparatus or the associated technique, e.g., “atomic force microscopy.”

As with most measuring devices, AFMs often require a trade-off betweenresolution and acquisition speed. That is, some currently available AFMscan scan a surface with sub-angstrom resolution. These scanners arecapable of scanning only relatively small sample areas, and even then,at only relatively low scan rates. Traditional commercial AFMs usuallyrequire a total scan time typically taking several minutes to cover anarea of several microns at high resolution (e.g. 512×512 pixels) and lowtracking force. The practical limit of AFM scan speed is a result of themaximum speed at which the AFM can be scanned while maintaining atracking force that is low enough not to damage or cause minimal damageto the tip and/or sample. Great strides have been made in this area inwhich SPM has achieved video scan rates with high resolution for smallsamples and small scan sizes.

Nonetheless, given current limitations associated with known modes ofoperation, including both TappingMode™ AFM and contact mode,improvements have been desired. Again, in contact mode, lateral scanningof the tip creates large forces between the tip and sample that cancompromise both. And when imaging soft samples such as biologicalsamples and polymers, the surface can be destroyed, rendering themeasurement useless, or at least deformed severely, therebysignificantly compromising resolution. Note that “imaging” is usedherein to indicate obtaining SPM data at multiple points of a samplesurface, typically by providing relative scanning motion between thesample and probe and correspondingly interacting the sample and probe.

TappingMode™ AFM is a lower force technique and is the most widely usedmode of AFM operation to map sample surfaces, especially for delicatesamples. The typical force of the tip on the sample is about a few nN totens of nN. Again, by oscillating the tip, rather than dragging the tip,the shear forces are minimized. That said, TappingMode™ AFM suffers froma drawback in that it is difficult to control the normal force acting onthe sample surface. The user typically tries to select a setpoint thatis only a small variation from the free air deflection/amplitude of theprobe in order to minimize tip-sample interaction forces to get the bestreproduction of the sample profile. The dilemma, especially for softsamples, is that if the imaging force is too low, the tip will not trackthe sample properly (i.e., maintain interaction with the sample duringthe scan), while if too high, damage/deformation of the sample may leadto an image that does not accurately reflect surface topography.Overall, the better this force can be controlled (i.e., the lower it canbe maintained) the less chance of sample and/or tip damage, and thusresolution can be improved.

A review of the tip-sample forces in each of these modes providesinsight in to the limitations of each. When a probe interacts with thesurface through TappingMode™ AFM or Jumping Mode™ (see, e.g., U.S. Pat.Nos. 5,229,606, 5,266,801 and 5,415,027, the entirety of which areincorporated by reference herein), the tip touches the surfaceperiodically. FIG. 2A illustrates the physical process within one period“T” of the tip motion. FIG. 2A shows tip trajectory in reference to thesample surface position. FIG. 2B shows the corresponding interactionforce at the same time for tip trajectory at various positions. At thepeak positions A_(max), the tip is farthest from the sample surface andnot interacting with the sample. As the tip continues to move downtoward the horizontal axis (zero tip-sample separation) it willexperience a near-field Van der Waals force, F_(a) _(_) _(vdw), causingthe tip to snap into contact with the sample through Van der Waalsattraction. After touching the sample, the tip remains in repulsiveinteraction for time zone δT. During this time, the tip is continuouslycontacting the sample. The positions below zero represent that the tipmay have deformed the sample, causing its position to be shown below thesample surface.

As the tip departs the surface after δT, an attractive force willdevelop a capillary meniscus, exhibiting a maximum adhesion force F_(a)_(_) _(max) right before the meniscus is broken away. The tip thenenters into a non-interactive region and continues to a maximumdeparture position.

In the interaction free zone, when the probe is farther from thesurface, the interaction force is zero or sufficiently near zero to forma baseline, as indicated in FIG. 2B. In FIG. 2B, the force above thehorizontal axis is repulsive while those points below the horizontalaxis represent a net attractive or adhesive force. The maximum repulsiveforce F_(r) _(_) _(max) usually corresponds to the lowest or smallesttip position or separation relative to the sample surface.

In prior known modes disclosed in TappingMode™ AFM and JumpingMode™ AFM,the amplitude A_(max) or RMS of the tip oscillation amplitude is used asthe feedback control parameter. An example of such feedback controlapparatus is shown in FIG. 1.

In conventional control, typically implemented using a gain controlfeedback loop, positioning actuators and a cantilever response detectioncomponent (quadrant photodetector, for example), the AFM uses detectedprobe deflection or an RMS signal corresponding to cantilever (i.e.,probe) motion as an indication of the tip-surface interaction and usesthe feedback loop to maintain constant or RMS deflection.

Yet a major limitation of conventional AFM is its inability to acquirequantitative mechanical property information simultaneously with thehigh-resolution imaging. AFM has been primarily focused on topographicalimaging. Little progress has been made in achieving quantitativemechanical mapping, including elasticity, plasticity, and work ofadhesion.

Moreover, TappingMode™ control uses amplitude or phase of the measureddeflection signal to control tip-surface interaction using feedback.Notably, both amplitude and phase are average properties of theprobe/tip oscillation using at least one cycle of interaction. Morespecifically, the average pertains to probe/sample interactionsoccurring in all the positions in the tip trajectory (FIG. 2).Therefore, there is no possibility for the control feedback to be basedon substantially instantaneous tip-sample interaction. Note thatinstantaneous interaction here refers to any point (for example, withintwo microseconds) of interaction in FIG. 2B (discussed further below).

In addition, it is important to note that TappingMode™ AFM was createdto overcome what is known as the stick-in condition that occurs whenprobe touches the sample intermittently. As the probe touches thesample, capillary force will tend to catch the tip and prevent it fromreleasing. The amplitude of probe oscillation in TappingMode™ will dropto zero, thereby causing feedback oscillation. This problem was overcomewhen using TappingMode™ by using probes having a certain stiffness,usually 10 N/m (Newton/meter) to 60 N/m, with a nominal value of 40 N/m,while operating the TappingMode™ AFM at an oscillation amplitude higherthan about 10 nm peak-to-peak. Under these conditions, as the probetouches surface, the kinetic energy of the tapping probe coverts toenough static elastic energy to overcome the capillary force, assuringsteady amplitude in each cycle. One drawback of this mode is that thekinetic energy stored in the probe is also proportional to thecantilever spring constant. When employing a lower spring constantcantilever, such as 1 N/m, TappingMode™ is impossible when measuringmany materials because the cantilever cannot overcome the capillaryadhesion forces using its own resonance oscillation energy.Consequently, most TappingMode™ applications are only possible when oneuses a stiff cantilever generally known in the art as a lever.

In an alternate mode of operating an SPM, known as the pulsed-force modeor PFM (see, e.g., U.S. Pat. No. 6,880,386 and U.S. Pat. No. 7,129,486),the amplitude of the oscillation of the probe is adjusted so the tipgoes in and out of contact during each cycle. In this mode, control isprovided by monitoring tip-sample interaction forces. It operates basedon properties associated with a force curve, another common measurementmade in the AFM field to measure material properties at a particularlocation. Force measurements are common, and can be mapped over anentire sample to create what is known as a force-volume image.

In PFM, by analyzing the shape of the force-distance curve, and usingthe data to control the forces acting between the tip and the sample,the amount of data acquired is lessened compared to other modes of SPMoperation. Importantly, PFM typically needs to operate at F_(r) _(_)_(i) (discussed below) or the peak pulse force, which substantiallyexceeds the adhesion induced deflection, as well as coupling induceddeflections. As a result, a high repulsive force is needed as a controlreference. Such high force could damage the sample or the tip, and thusprevent acquisition of high resolution images. Moreover, PFM has otherlimitations, particularly with respect to operating speed and resolutionlimitations, and thus, though it has been implemented to image softsamples, it has not been more widely adopted for all types of AFMimaging applications. In addition, when imaging in a fluid environmentprovide further challenge to PFM since viscous force in fluid produceslarge deflection even when the cantilever probe is not interacting withthe sample.

More particularly, a main reason why imaging speed is limited instandard PFM AFM is illustrated in FIG. 2C. FIG. 2C is a graph oftip-sample interaction force versus time. The interaction force isplotted as snap-to-contact at “A”, at which point repulsive force(sample on tip) initiates at “B.” Peak repulsive force occurs at about“C” as adhesive forces pull on the tip until about point “D”, the pointat which the tip releases from the sample. Point E represents thedeflection peak of the cantilever probe when it departs from the sample.Points C and E both present themselves as a peak in the deflectionsignal. In order to assure that feedback controls tip-sample interactionproperly, the value of C should exceed E. In yet another constraint inPFM, a certain ringdown period (cycles of the probe oscillation at itsresonance frequency) is required before it is possible to determine thebaseline force needed to continue the scan. It is this waiting for thecantilever to “ringdown” (a free decay process, as in TappingMode™) thatlimits the modulation frequency, and thus scan speed. More particularly,modulation frequency is significantly less than the probe resonancefrequency (for example, a fifth or more below the probe resonancefrequency).

SUMMARY OF THE INVENTION

The preferred embodiments move the tip substantially perpendicularly tothe sample surface to cause the tip to interact with the sample, andthen depart from the sample. The embodiments control the feedback loopusing instantaneous interaction force (e.g., substantially orthogonal tothe sample surface) at any interaction point, preferably using themaximum repulsive force. This new mode of operation takes advantage ofthe instantaneous response of the probe upon tip-sample interaction (noneed to wait for ringdown like prior techniques, the present techniquedetermines a baseline or zero force reference and forcefullysubstantially instantaneously brings the tip back to the surface), usingthe feedback loop to maintain a steady state interaction, and to controltracking of the tip on the sample. By moving the tip perpendicularly tothe sample surface, this mode shares the advantages of TappingMode™ AFMto at least substantially eliminate friction forces during rasterscanning or other relative probe sample motion in the XY plane. Inaddition, the implementation of this mode minimizes parasitic couplingso that a far more sensitive force control than PFM and TappingMode™ AFM(at least three (3) orders magnitude), can be accomplished. In doing so,the lowest force imaging (using alternating force) known in the AFM artis realized and directly controlled, thus allowing the AFM to provideimproved high resolution images even higher than TappingMode™ AFM atspeeds exceeding typical TappingMode™ AFM speeds (about 1 kHzbandwidth). An added benefit is that each cycle of the vertical movementproduces a force curve, or multiple force curves at each pixel, allowingsimultaneous acquisition and mapping of height and mechanical propertydata. This method is therefore called Peak Force Tapping (PFT) modesince it generates and analyzes each and every individual force curve,then measures and controls the corresponding peak interaction forcesduring each tip tapping on the sample with imaging speed higher thanTappingMode™ imaging speed.

In accordance with a first aspect of the invention, a method ofoperating a SPM includes generating relative motion between a probe anda sample and detecting motion of the probe. The method recovers, fromthe detected probe motion, a probe-sample interaction that issubstantially independent of parasitic probe deflection (i.e., parasiticcantilever motion).

In another aspect of the invention, a method of operating a SPM includesgenerating an image while maintaining a maximum repulsive probe-sampleinteraction force of no more than about 10 pN during each cycle ofsubstantially perpendicular cyclical movement of the tip relative to thesample. Such interaction force can be directly controlled and accuratelycalibrated.

According to another aspect of the invention, a method of operating anSPM includes generating an image for at least 1 hour with peak force ofless than 5 nN, without user intervention, while maintaining an imageresolution better than 5 nanometers regardless of environment, includingambient, gaseous, fluid and vacuum.

In another aspect of the invention, a method of operating an SPMincludes generating at least one force-distance curve for each imagingpixel. The force-distance curve can be used to produce accuratemeasurement of one or more of Van der Waals adhesion, elasticity, workof adhesion of tip-sample interface, plasticity such as hardness andviscoelasticity.

According to another aspect of the invention, the Peak Force Tappingmethod of operating an SPM includes using cantilevers with springconstants equal to about 0.01 N/m to 1000 N/m (which can enable thecapability to map mechanical properties over a range from about 10 kPato 100 GPa). This range of applicable cantilevers is several orders ofmagnitude wider than cantilevers generally applicable to ContactMode AFM(0.01-1 N/m) and TappingMode™ AFM (1 N/m-40 N/m).

A SPM configured in accordance with the invention could be used to scana wide variety of samples, including patterned wafers, biologicalsamples in ambient and fluid, polymers, thin films, and data storagedevice component.

According to a further aspect of the invention, a method of operating aSPM includes interacting a tip of a probe with a sample, thenterminating the interaction, resulting in a decaying probe oscillation.Thereafter, the method repeats the interaction before ringdown of thedecaying probe oscillation is substantially complete, and detects themotion of the probe.

In another aspect of the preferred embodiments, a scanning probemicroscope (SPM) includes an actuator to generate relative motionbetween a probe and a sample, and a detector to detect motion of theprobe. A digital controller is also included to determine, from thedetected probe motion, a probe deflection based on a probe-sampleinteraction, the probe deflection being substantially independent ofparasitic probe deflection. Notably, the parasitic probe deflection iscaused by the background associated with operation of the SPM, andcorresponds to any relative periodic motion between the probe and thesample when the probe is not interacting with the sample. The controllersubtracts the background from the detected probe motion, and controlsthe SPM in real time using the probe deflection.

These and other features and advantages of the invention will becomeapparent to those skilled in the art from the following detaileddescription and the accompanying drawings. It should be understood,however, that the detailed description and specific examples, whileindicating preferred embodiments of the present invention, are given byway of illustration and not of limitation. Many changes andmodifications may be made within the scope of the present inventionwithout departing from the spirit thereof, and the invention includesall such modifications.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred exemplary embodiments of the invention are illustrated in theaccompanying drawings in which like reference numerals represent likeparts throughout, and in which:

FIG. 1 is a block diagram of a conventional atomic force microscope,appropriately labeled “Prior Art”;

FIG. 2A is a graph of tip-sample separation versus time in oscillationAFM modes;

FIG. 2B is a graph of interaction force versus time in oscillation AFMmodes;

FIG. 2C is a graph of an SPM force curve illustrating probe sampleinteraction, “ringdown” an illustration of a second probe sampleinteraction;

FIG. 3 is a graph of force versus time illustrating determininginstantaneous force for feedback control according to the preferredembodiments;

FIG. 4A is a schematic graph illustrating probe deflection versus timeillustrating tip sample interaction force modulated periodically withparasitic oscillations in the system;

FIG. 4B is a schematic of cantilever probe response versus time withonly hydrodynamic background oscillation due to parasitic sources;

FIG. 4C is a graph of deflection error versus time after subtraction ofhydrodynamic background oscillation;

FIGS. 5A-5C is a series of graphs of a) deflection response beforebackground subtraction, b) the subtracted background and c) thedeflection error versus time after subtraction of hydrodynamicbackground oscillation;

FIG. 6A is a schematic illustration of force versus time illustratingthe baseline averaging method of the preferred embodiments;

FIG. 6B is a graphic illustration of tip-sample separation versus time;

FIG. 6C is a graphic illustration of cantilever deflection versus time;

FIG. 7 is a schematic graph of force versus time illustrating the priorart technique of averaging to a force over an entire cycle (RMS) todetect tip sample interaction;

FIG. 8A is a schematic force versus time curve illustrating the gatedaverage repulsive force control according to the preferred embodiments;

FIG. 8B is an illustration of an input synchronization signal sent withthe force response due to tip-sample interaction to realize gatedaverage repulsive force control according to the preferred embodiments;

FIG. 9A is a schematic illustration of a series of force curves used insynchronous averaging according to the preferred embodiments;

FIG. 9B is a graph illustrating a synchronization signal sent with thedeflection applied in the force curve of FIG. 9A;

FIG. 9C is a graph illustrating a force curve signal after severalcycles of synchronous averaging of FIG. 9A;

FIG. 10 is a schematic block diagram of an AFM operable in PFT Mode,according to one embodiment;

FIG. 11 is a flow diagram illustrating a method according to thepreferred embodiments;

FIG. 12A is a schematic graph of a force curve illustrating the systemsetpoint and measured deflection;

FIG. 12B is a schematic illustration of the feedback error producedaccording to prior art methods that control AFM operation by triggeringon force after completion of one modulation cycle;

FIG. 12C is a schematic illustration of the feedback error, similar toFIG. 12B, according to the preferred embodiments of the presentinvention;

FIG. 13 is a flowchart illustrating a method according to the preferredembodiments illustrating deflection background subtraction;

FIG. 14 is a flow diagram illustrating cantilever deflection backgroundsubtraction using a lock-in amplifier, according to the preferredembodiments;

FIG. 15 is a flow diagram illustrating deflection background subtractionin a normal engage process;

FIG. 16 is a flow diagram illustrating deflection background subtractionin a sewing engage process;

FIG. 17 is a graph of force versus time illustrating baselinecalculation according to the preferred embodiments;

FIG. 18 is a graph of force versus time illustrating an algorithm usedto determine instantaneous interaction force;

FIG. 19 is a flow diagram illustrating a method of instantaneous forcecontrol imaging;

FIGS. 20A and 20B are graphs illustrating force versus time and zposition respectively, when using instantaneous force control imagingaccording to the preferred embodiments;

FIGS. 21A and 21B are AFM images illustrating deep trench measurementsusing TappingMode™ AFM and instantaneous force control mode according tothe preferred embodiments;

FIG. 22A is a graph of force versus tip-sample separation, illustratingsmall amplitude repulsive force mode (SARF) according to the preferredembodiments;

FIG. 22B is a graph illustrating force versus time for the SARF mode;

FIG. 23A is a graph of force versus tip-sample separation, illustratingsmall amplitude attractive force mode (SAAF) according to the preferredembodiments; and

FIG. 23B is a graph illustrating force versus time for the SAAF mode.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The preferred embodiments are directed to a Peak Force Tapping® (PFT)Mode of AFM operation in which the interaction force between the probe(tip) and sample is monitored and used to control tip-sample separationat very low forces, yet without compromising scanning speed. Thetechniques described herein provide high resolution by maintaining probetip-sample forces low, and realizes essentially real-time propertymapping of sample surfaces. The preferred embodiments are inherentlystable and thus facilitate long-term force control while maintaining theability to acquire high integrity data (improved resolution). Moreover,because tuning is not required, unlike conventional TappingMode™ AFM,the AFM setup is faster and easier than with other AFM modes. The keyconcepts driving the PFT Mode are illustrated graphically and discussedherein.

Practically, there were three major issues to be resolved before AFMcontrol using instantaneous interaction force could be implemented.These issues were 1) accommodation of deflection background due tocoupling; 2) determination of a baseline; and 3) determination of theinstantaneous force, as defined herein.

In FIG. 2A, a cycle of modulation that approaches and separates theprobe from the sample (for example, using a drive to cyclically modulateprobe-sample separation) is represented by a period T. The zero position(horizontal axis) represents the surface while the vertical axis is theseparation. When the probe-sample separation crosses the horizontal zeroline, the tip is in direct contact with the sample, as represented byregion δT (the window of tip-sample contact). The interaction forcecorresponding to this region is plotted in FIG. 2B.

With further reference to FIGS. 2A and 2B, A_(max) is the maximumseparation of the tip apex from the sample; F_(a) _(_) _(vdw) is the Vander Waals adhesion force; and F_(a) _(_) _(max) is the maximum adhesiondue to capillary interaction and work of adhesion between the tip andthe sample surface. Both repulsive force and adhesive force arecalculated relative to the baseline as shown in FIG. 2B. It should benoted that the force referenced here is the total force acting on theentire tip which is typically, pyramidal-shaped. In fact, the very apexportion can enter the repulsive zone while the total force remainsattractive. In this case, the feedback can still use the apex repulsiveinteraction force at the predefined synchronization position (defined asdiscussed below) for feedback, even though the total force at this pointis attractive. This provides the benefit of operating with the minimuminteraction force with the highest imaging resolution since the controlis determined by the apex repulsive interaction which arises from thePauli and ionic repulsions between the atoms of very apex of probes andthe atoms or molecular of samples.

It is important to differentiate cantilever deflection and tip-sampleinteraction force. While cantilever deflection is used to gauge thetip-sample interaction force, not all the deflection representstip-sample interaction force; namely, parasitic forces contribute tocantilever deflection. For example, as shown in FIG. 2C, the cantileverdeflection is plotted as a function of time, the figure representingactual deflection data. The oscillation after point “D” is due tocantilever free resonance decaying with time. This resonance deflectionis not caused by tip surface interaction and is considered a parasiticdeflection contribution (typically corresponding to parasitic cantileveror probe motion). Point E represents a maximum point of deflection atwhich the tip is not interacting with the sample. The “flat” portion ofdata also could have a slower variation of the deflection, when the tipis not interacting with the sample, typically caused by mechanicalcoupling of parasitic forces. Such coupling could be due to themodulation actuator itself, and/or cantilever response due to dampingforces from air or fluid. It can also arise from laser interference.These parasitic effects will be further illustrated in subsequentfigures.

In known force control systems, the control is based on a maximum forceoccurring in a period. Hence the repulsive force must be higher than anyof the parasitic contributions to deflection for true tip-sampleinteraction to be differentiated from parasitic forces and historicallyused by the feedback loop. This force differentiation requirementrequired a relatively high imaging force that could damage the tipand/or the sample, thereby preventing the system from achieving highresolution.

In a preferred embodiment, the RMS or constant deflection is replaced byan instantaneous interaction force F_(r) _(_) _(i), determined accordingto FIG. 3, with the controller setpoint being:δFr=F _(r) _(_) _(i) −F _(baseline)  Equation (1)F_(baseline) is the interaction force when the probe is not contactingthe sample. It should be zero. In AFM, the force is usually representedby cantilever deflection. In this case, F_(baseline) corresponds to thecantilever deflection when the tip is not interacting with the surface.F_(r) _(_) _(i) is the interaction force when the tip is at closeproximate contact with the surface. A synchronization algorithm is usedto align the start time of each drive period, so that the region δT(FIGS. 2A-2B) coincides with the repulsive force and its maximum F_(r)_(_) _(max). The time from the start of the period to the occurrence ofthe F_(r) _(_) _(max) is the synchronization time, which can beprecisely determined and controlled (described further below).Synchronization time distance (Sync Distance) can be determined bymeasuring the phase delay between the deflection response and themodulation drive signal. Once the Sync Distance is determined (when theprobe is stationary in the xy direction), the same Sync Distance is usedthroughout all xy raster scanning positions. During imaging, thefeedback operates to maintain F_(r) _(_) _(i) substantially constantwhile the value of F_(r) _(_) _(i) is determined by the Sync Distance.Note that the Sync Distance can also be generalized as the distance fromthe starting of the modulation period to the instant of interaction.

The synchronizing distance or Sync Distance can be precisely controlled.For example, if the tip oscillation period T is 100 μs, when thesynchronizing distance is 48 μs, the interaction force occurring at the48th μs will be used as the feedback control parameter. The feedbackloop will try to maintain an instantaneous interaction force F_(r) _(_)_(i) (i=48 μs) at the 48th μs from the start of the period. In moregeneral applications, any point of interaction force within theinteraction region δT can be used for feedback. δT can also extendsbeyond the marked region in FIG. 2B to include the region of F_(a) _(_)_(vdw) (van der Waals attractive region) and F_(a) _(_) _(max) (thecapillary adhesive region). The capillary adhesive region can also beadhesive interaction due to bonding force induced by functionalizedprobes and specific bonds on the sample.

To achieve an accurate measurement of the baseline, multiple deflectiondata points are gathered when the tip is not interacting with the sampleand used to generate an averaged baseline level. Again, thenon-interaction region (greatest separation/highest distance) can bedetermined by the Sync Distance because this region should be around thehalf cycle of the modulation period after the peak force position. TheSync Distance also determines the feedback force operating point, andthe actual force is measured by δFr. δFr can be either negative orpositive.

Due to adverse affects of drift (e.g., thermal) on the deflection, thecorresponding force F_(r) _(_) _(i) may vary over time. The relativeforce δFr (relative to baseline determination) preferably is used forfeedback control instead of F_(r) _(_) _(i) because it is a moreaccurate reflection of tip-surface interaction. This relative valueremoves the adverse influences due to system drift on cantileverdeflection.

δF_(r) also represents a controllable force by the feedback loop suchthat δF_(r) remains constant over time at various positions as the tipscans across the sample.

In FIG. 4A-4C, the cantilever response, when interacting with the samplesurface, is a mixture of the tip-surface interaction force and thebackground coupling. Such response is exhibited schematically in FIG. 4Aas “Original.” The real tip-sample interaction force is only at theF_(r) _(_) _(i) portion (shown in 4C), which is buried within thebackground of parasitic cantilever or probe motion. By subtracting thebackground from the original data (for example, probe motion includingdue to both interaction forces and parasitic forces), the magnitude ofthe interaction force can be obtained. The background, illustrated as4B, can be caused by mechanical coupling of resonances from the AFMsystem, and/or cantilever response to its environmental medium, such asair and fluid. It can also be induced by laser interference as thecantilever moves relative to the sample. The common characteristic ofthe background is that cantilever deflection displaying periodic changeis similar to the tip trajectory, even when the tip is not interactingwith the sample. A successful subtraction of background experimentaldata is shown in FIGS. 5A-5C.

More particularly, FIG. 5A shows a schematic illustration of theoriginal probe deflection versus time. As noted, the deflection of theprobe is highly influenced by parasitic sources that may be used tocontrol tip-sample interaction. As shown, these periodic parasiticdeflections are represented by the low frequency signal that we refer toherein as the “hydrodynamic background,” for example or parasitic forcein a more general term. The contribution to the probe deflection bythese parasitic forces (including hydrodynamic forces, drag forces andair, off-axis motions, laser inference and any other periodic motionoccurring when the probe is not interacting with the sample) is large.The actual tip-sample interaction force which should be used as thecontrol signal in the preferred embodiments is superimposed on theparasitic background signal (FIG. 5B), so it can be a challengedetecting the actual tip-sample interaction forces. Stated another way,the minimum controllable force is determined by the backgroundcontribution to probe deflection (shown in FIG. 5A as the Min.Controllable Force_(OLD)—range of about less than 1000 micro-newtons toless than 10 pico-newtons). Notably, as is always the case, a noisesignal “N” having a low amplitude relative to both the parasitic forcecontribution to the deflection and the contribution to the deflection bythe tip-sample interaction force, is present.

Turning to FIGS. 5B and 5C, one key concept to the present preferredembodiments is the subtraction of the parasitic background signal (FIG.5B) from the deflection signal, as noted, thereby lowering the minimumcontrollable force. The background signal is determined by increasingtip-sample separation sufficiently to a controlled distance so that theprobe does not interact with the sample, i.e., only parasitic forces arecontributing to the detected deflection of the probe. The controlleddistance is typically greater than 100 nm, though it can be less,ideally being a distance at which long range interaction forces do notcontribute to probe deflection. As shown in FIG. 5C, the tip-sampleinteraction force contribution to the deflection after subtracting theparasitic background renders a deflection signal having clear peaksassociated with the tip-sample interaction. Notably, the non-periodicnoise will always be present, and in this case, determines the minimumcontrollable force as shown in FIG. 5C (Min. Controllable Force_(NEW)).For a very soft cantilever with a spring constant of 0.01 N/m andcantilever length of 100 um, this force can be about 1 pN.

It becomes clear that the minimum controllable force employable whenperforming parasitic background subtraction is lessened greatly (by, forexample, three (3) orders of magnitude), allowing the preferredembodiments to control tip-sample separation so the probe-sampleinteraction forces are reduced to the pN range. The way in which thissubtraction may be accomplished in the hardware is described furtherbelow with respect to FIG. 10.

Overall, it is primarily this ability to detect such small forces, andto use such forces as a control parameter in an SPM feedback loop, thatallows an SPM operating according to the present invention to image asample using what is referred to herein as “instantaneous forcecontrol.” Instantaneous force control using real-time force detectionoffers improved control, thus improving image resolution and minimizingthe chance for sample damage. In this context, real-time orinstantaneous force detection implies that essentially each point of thevarying force illustrated, for example, in FIG. 3 can be detected by thepreferred embodiments and used instantaneously to control SPM operation.In other words, the varying forces acting on the probe due toprobe-sample interaction during each cycle of the interaction betweenthe probe and sample [or during each cycle of the modulation of theseparation between the two, i.e., the force curve modulation] aredetected and may be used by the AFM to image the sample in real-time.This instantaneous force control is used to provide AFM control at anyinteraction point within what would be one cycle of the modulation ofthe probe-sample separation. Because control is provided prior tocompletion of any would-be cycle of modulation (prior to the nextapproach), the feedback delay is greatly reduced. This will be shownfurther in connection with FIGS. 12A, 12B and 12C.

Yet another benefit in the peak force tapping control is that it doesnot need to be operated near the cantilever resonance frequency. Suchoperation can substantially eliminate cantilever delay due to transientresonance response, rendering instantaneous interaction controlpossible.

Turning next to FIG. 6, the preferred embodiments also allow the AFM tooperate at high speed by performing baseline averaging of the forcecurve to extract a zero force point quickly, and allow the system tocause the probe to interact with the sample with little time delay. Incontrast to prior techniques represented by FIG. 2C, the modulationfrequency of the present AFM is not limited by the requirement that thesystem wait to re-establish probe-sample interaction until probe“ringdown” completed (after the tip jumps off the sample surface, thedecaying of probe oscillation to about 1/e) to stabilize the imagingsystem. The time required for ringdown is determined by the cantileverdynamics which are proportional to Q/f, where Q is the quality factor ofthe cantilever and f is the cantilever resonance frequency—typicallytens of milliseconds for a conventionally used cantilever to stabilize.In the preferred embodiments, as shown in FIG. 6, upon ringdown, a fewcycles of the cantilever resonance frequency are averaged to determine azero force point (i.e., an at-rest baseline position) in essentiallyreal time, and allow the system to cause the probe to interact with thesample much quicker than the system illustrated in FIG. 2C. In fact, byconducting an average of even one cycle of the cantilever resonancefrequency upon ringdown, a robust estimation of the zero point(baseline) can be realized. As a result, modulation frequency can beincreased significantly without compromising system stability. Moreover,the added benefit of operating faster, of course, is reducing the effectof noise within the system.

For measurement with very sensitive force detection, very softcantilevers (spring constant 0.01 N/m to 0.3 N/m) are typically used.These levers have lower resonance frequency and very long ringdown time.More importantly, the adhesion induced oscillation (snap out of contact)is much stronger, as shown in FIG. 6C. In FIG. 6C, the deflectionresponse of a soft cantilever is plotted as a function of time. The tiptrajectory is also plotted as a position reference (FIG. 6B). As can beseen, the parasitic oscillation of the cantilever far outweighs theinteraction force, making control basically impossible. Previous to thepresent invention, a user would have to wait long enough for theoscillation to disappear so that F_(r) _(_) _(i) becomes the onlymaximum, in order to have a steady control of the feedback. As thecantilever gets more sensitive, waiting for ringdown becomesprohibitively time consuming. The preferred embodiments of the presentinvention determine the baseline by separating the interaction zone andnon-interaction zone through synchronous alignment to the closestposition between the probe and the sample. A region corresponding to an“interaction zone” is locked through a synchronous marker, a referencetrigger signal at the beginning of each cycle. Any point of deflectionin this region can be used as the feedback parameter for steady stateinteraction control. All deflection data outside the interaction zoneare averaged to a constant and used as the baseline for calculatingΔF_(r) in FIG. 3. By combination of the baseline detection andsynchronous control, the relative force 6F can be accurately determinedinstantaneously and controlled. Such control allows F_(r) _(_) _(i) tobe far below parasitic deflection, as illustrated in FIG. 6C.

Steady state again means a constant maximum force or a constant minimumforce, or a combination of the characteristics of the interaction forcecurve shape in each cycle of the probe/sample relative motion.

Another major advantage of the present techniques is the ability todetermine the baseline with high amplitude oscillatory data. Since theresonance frequency of the cantilever is known, in an alternativeembodiment, the average can be determined in the non-interacting zone byanalyzing an integer multiple of cycles of the cantilever resonancefrequency. The integer cycle averaging can effectively remove theoscillatory deflection data, yielding a constant baseline.

Notably, cantilever resonance frequency can also be determined by knowntechniques such as frequency sweep and thermal tune.

Turning next to FIGS. 7 and 8A and 8B, the preferred embodiments alsoemploy something referred to herein as “gated average repulsive forcecontrol.” FIG. 7 schematically shows probe deflection, including aseries of interaction periods, upon AFM operation. Prior controltechniques using force as a control parameter average the total forceover the entire cycle of tip-sample interaction, yielding an RMS valuefor comparison to the force setpoint. As understood in the art, theforces illustrated by the force curve are complex. Both repulsive andattractive forces operate on the probe tip during a cycle, as describedabove. By including, for example, the attractive force portion (C-D inFIG. 2C) which tends to cancel repulsive force, force sensitivity andimaging resolution are most often compromised.

Turning to FIGS. 8A and 8B, gated average repulsive force control isillustrated. In this embodiment, a system synchronization signal such asthat shown in FIG. 8B is used to “gate” the repulsive force portion (B-Cin FIG. 2C) of the force curve (illustrated by the shaded portion “A” ofthe deflection curve) by excluding the attractive force portion of theforce curve. By controlling tip-sample separation based on the repulsiveforce portion of the force curve, force sensitivity and imagingresolution are increased due to reducing the adverse effect of theattractive force portion of the curve (i.e., attractive interactionforces are long range interaction forces, and therefore senseinteraction over a much larger area, yielding lower resolution).Moreover, the gate operates to exclude the noise when performing thegated averaging. Again, the synchronization signal is timed so that onlythe repulsive force region is used. Such operation is ensured by usingthe gate at a pre-determined synchronization position as shown anddescribed in connection with FIG. 3.

Taking the above further, as shown in FIGS. 9A and 9B, synchronousaveraging can also be employed to further improve signal-to-noise ratio,and thus ultimately provide control at nearly the zero force point. FIG.9A, similar to the other tip-sample deflection illustrations, showsseveral cycles of deflection of the probe as the tip interacts with thesample. As noted previously, a noise signal is always present whenmaking these types of SPM/AFM measurements. By combining the deflectionsignal with a corresponding synchronization signal, such as that shownin FIG. 9B, synchronous averaging of the deflection is performed. As aresult, the effect of noise is reduced greatly according to,

$\begin{matrix}\frac{D_{1} + D_{2} + D_{3} + D_{4} + {\ldots\mspace{14mu} D_{N}}}{N} & {{Equation}\mspace{14mu}(2)}\end{matrix}$Where D_(i) representing data in the ith cycle. The averaged signal witha signal to noise ratio improved by a factor of √N, thereby reducing theminimum controllable force (can use narrow lock-in bandwidth), is shownon FIG. 9C.

Turning next to FIG. 10, an AFM 100 operable in PFT Mode includes aprobe 102 mounted in a probe holder 108 and having a cantilever 104supporting a tip 106. In this case, tip-sample separation is modulatedby an actuator 112 (for example, an XYZ piezoelectric tube) coupled tothe probe holder 108 thereby. However, it should be understood that thepreferred embodiments are applicable to those AFM instruments thatmodulate tip-sample separation by moving the sample in Z.

During operation, probe deflection is measured by bouncing a light beam“L” off the back of the probe and toward a detector 114, such as a fourquadrant photodetector. The deflection signal is then transmitted to ananalog to digital converter 103. The digitized signal is used formaintaining the tip-sample force low while operating the AFM at highspeed.

In the embodiment shown in FIG. 10, probe deflection without tip-sampleinteraction is transmitted to a background generator 105. The backgroundgenerator will create a periodic waveform corresponding to thebackground signal when the tip and sample are not interacting. Thiswaveform can be generated by a DDS (Direct Digital Synthesis functiongenerator) whose amplitude and phase are determined by a lock-inamplifier, and whose input is the background signal. This waveform canalso be generated by synchronously averaging multiple cycles of thebackground with the help of a synchronization signal. A comparatorcircuit 120 processes the total deflection signal by subtracting thebackground signal so as to generate a signal representative oftip-sample interaction force independent of the parasitic background(FIGS. 4C and 5C). (Note that, though analog or digital circuitry may bedescribed, it is understood that the operations may be performed in anyconventional analog or digital circuitry, though a preferred embodimentutilizes FPGA architecture to implement the invention). This signal isthen fed through a digital filter 122 that processes thepost-subtraction deflection error to limit the processed ringdownoscillation of the lever to a number of selected cycles. The filteredsignal is transmitted to synchronous averaging circuit 123 to furtherincrease the signal to noise ratio. By averaging data in thenon-interaction region with the help of synchronization, a baseline isdetermined from baseline averaging circuit 124. A comparator circuit 125processes the total deflection signal by subtracting the baseline signalso as to generate a signal representative of tip-sample interactionforce with no cantilever DC drift. This signal is further transmitted toa force detector 126.

Sync Distance calculator 135 determines the phase shift between thedeflection and the Z modulation DDS (Block 127) that provides the driveand synchronization control in the form of a time delay. Peak force orrepulsive force gate position generator 129 generates the timing signalfor force detector 126, with the help of the synchronization marker andsynchronization time distance. Force detector 126 analyzes the output ofsummation circuit 125 by either identifying the repulsive peak force oraveraged repulsive force within the gated region illustrated in FIG. 8A.Again, by operating force detector 126 this way so force control can betriggered on a selected part of the force curve (e.g., repulsive forceregion), higher sensitivity is achieved by reducing the effect of theattractive force between the sample and tip. Moreover, signal to noiseratio is improved by excluding noise from the gate of detector 126. Thegated repulsive force is then compared to an appropriate setpoint (Block128), and an error signal is generated and transmitted to a controlblock (e.g., a PI controller 130). The control signal is then convertedto analog (converter 132) and transmitted to a summing circuit 134 forcombination with a synchronization signal from Block 127 after thesynchronization signal is converted to analog with a converter 136. Theoutput of summing circuit 134 is then applied to the Z-piezo 112 foractuating the z position (in this case, the probe) to maintainessentially steady state interaction between the tip and sample. Acorresponding method of operation is described in further detail belowin connection with FIG. 13.

Turning to FIG. 11, a method 300 of operating an AFM according to PFTMode is shown. After a setup and initialization Block 302 (no tuningrequired), the probe is driven into oscillation and engaged with thesample. Preferably, in Block 304, relative XY motion between the probeand sample is initiated (scanning).

Motion of the probe is then detected; in particular, probe deflection isdetected and transmitted to the converter for further processing. InBlock 306, the method then operates to recover probe-sample interactionas described above, preferably performing hydrodynamic backgroundsubtraction using either lock-in amplification, or more preferably,synchronous averaging of the deflection. After filtering the output inBlock 308 (e.g., selecting a number of cycles of ringdown to process),the method detects the force (peak force detection/gated averaging),preferably using the repulsive region of the force curve, in Block 310.In Block 312, the force is then compared to the setpoint force, setaccording to the user's desired interaction force. The Z-actuatorresponds to the control signals in Block 316 to adjust tip-sampleseparation and maintain the setpoint force, with the control signalsbeing used to generate an image of the sample.

Turning to FIGS. 12A-12C, an illustration of the ability of thepreferred embodiments to provide instantaneous force feedback is shown.In FIG. 12A, several schematic force versus time curves are shown withdifferent peak repulsive forces. Notably, interactions Q and S exceedthe threshold force defined by the setpoint, while interaction Rillustrates a peak repulsive force below that of the setpoint. Thefeedback error is illustrated as shown in FIG. 12B for prior art forcefeedback systems. More particularly, once the repulsive force exceedsthe setpoint, a delay “d” is shown prior to mapping peak repulsive forceat X for the first interaction. This is similar for the interactionlabeled S in which the feedback error is not established until wellafter the point at which the repulsive force begins to exceed thesetpoint.

To the contrary, as shown in FIG. 12C, the response to any force largerthan the setpoint is detected essentially instantaneously, given lessfeedback delay due to the features of PFT Mode discussed above,including parasitic background subtraction, baseline averaging and gatedaverage, repulsive force control, preferably in combination withsynchronous averaging. By being able to quickly identify forces abovethe setpoint, the forces corresponding to tip-sample interaction can beminimized, thus providing a significant advantage in terms of AFMoperation at high speed and high resolution. And this is especially truefor rough samples in which sample surface changes can limit responsetime and/or resolution.

Algorithms

To assure accurate subtraction of the background, two schemes have beendeveloped, as shown in FIG. 13 and FIG. 14.

In FIG. 13, an algorithm 400 for the subtraction of cantileverdeflection background (parasitic contributions to deflection) is shown.Blocks 402 and 404 assure the tip is far enough away (30 nm, forexample) from the sample so that there is no repulsive impulseinteraction on the surface, according to a user selection upon set up.Block 406 contains several sub-steps. The AFM system samples cantileverdeflection data for multiple cycles and digitizes the data into multiplesegments with each segment having a period T. The AFM method aligns eachsegment of data to the start of the period T, and then averages thedata. Next, method 400 uses the averaged segment data as the backgroundfor the period T. Block 408 operates to subtract the background obtainedfrom Block 406 from the measured data in each period T using, forexample, an FPGA processor. Block 408 uses the background corrected datafor feedback.

In FIG. 14, another algorithm 500 for subtracting background deflectionis shown. Blocks 502 and 504, calculating lift height and lifting thetip with z feedback off, are used to ensure the tip is not interactingwith the sample. Block 506 uses a lock-in amplifier with the drivesignal moving the cantilever probe as the reference, and the cantileverdeflection data as the lock-in input. In Block 508, the amplitude andphase data obtained from lock-in are used to construct a sinusoidalsignal, and this signal is adjusted and used to subtract the deflectiondata until deflection becomes a constant (within the noise limit). Realtime subtraction is performed in Block 510. Once sufficient subtractionis achieved (determined using a constant deflection when the tip is notinteracting with the surface), the AFM is able to use the backgroundcorrected data for feedback in Block 512.

The background calculated according to FIGS. 13 and 14 variessubstantially as the probe approaches the sample surface. Such variationis caused by hydrodynamic force as a function of the probe to samplesurface distance. Such variation can also serve as an indicator of thecloseness of the probe to the sample before it actually interacts withthe sample. With this knowledge, the motorized engaging can proceed at afast speed until a pre-defined background value is reached; slowerengage steps can then be performed.

Background subtractions are preferably also executed during engagementof the probe with the sample surface, as shown in FIGS. 15 and 16.

The difference between the two engage methods is that the “normal”engage 600 in FIG. 15 uses a step motor only to drive the probe towardthe sample to detect the sample surface. However, FIG. 16 shows a“sewing” engage that moves the probe with the Z-piezo at each motor stepas the method 700 searches for the sample surface. Referring initiallyto FIG. 15, method 600 initially steps, in Block 602, a motor to reducetip-sample separation according to a fixed step of, e.g., 0.1 nm toabout 3 microns. With feedback control on (force detection according tothe present techniques), the feedback loop controls the actuator to movethe tip, in this case, toward the sample in Block 604. In Block 606, thealgorithm determines whether the surface has been detected (i.e.,whether the threshold setpoint force has been reached). If not, abackground subtraction operation as described above in connection withFIG. 5 is performed prior to further stepping the motor in Block 602. Ifso, feedback is disengaged, and a lift height is computed by calculatingthe z movements between peak force and maximum negative adhesion forceposition, plus a certain margin (for example, 10 nm), and the tip can beraised in Block 610 (e.g., to minimize the chance of crash). Thereafter,in Block 612, a background subtraction operation is performed, andfeedback control according to the present techniques is again initiatedin Block 614.

In FIG. 16, Blocks 708, 712, 714 and 716 correspond directly with Blocks606, 610, 612 and 614 of the algorithm 600 of FIG. 15. However, prior todetecting the surface, a sewing engage such as that known in the art isemployed to lift the tip in Block 702 prior to stepping the motor downin Block 704; in this case, the lift is 1.5 times the motor step. Theamount of lift may be user-selected based on type of sample, etc.Thereafter, feedback is turned on in Block 706 to detect force accordingto the present techniques. If the surface is not detected, the algorithm700 performs a background subtraction in Block 710 (similar to Block608) prior to conducting another lift in Block 702. Once the surface isdetected, the SPM can image the sample in Block 716.

FIG. 17 illustrates a practical situation of the tip-sample interaction,and provides a supplemental discussion to the above in connection withFIG. 6. The real tip-sample interaction occurs only in the vicinity ofthe Sync Distance marker. In the interaction free region there is aresidual self-oscillation of the cantilever due to break-off of theadhesion force (aka, ringdown). Such oscillation causes baselinefluctuation, rendering the same fluctuation of δFr shown in FIG. 3. Suchvariation will become controller noise. In order to minimize baselinefluctuation, the data marked as within the “baseline average” region areaveraged into a single constant, represented by the dashed line. Thisconstant data is used as the baseline in calculating δFr in eachfeedback cycle. The region for “baseline average” can vary depending onthe data quality. It needs to be smaller than the Sync Distance to avoidaveraging the real tip-sample interaction occurring at about the SyncDistance.

The instantaneous interaction force can be determined by using the forceδFr calculated by Equation (1), in which F_(r) _(_) _(i) can be aninstant value at the Sync Distance. As illustrated in FIG. 18, it canalso be a value determined through a gated average (see also FIGS. 7 and8A/8B). The gated average scheme uses the deflection values in the timezone δt and averages all data points in this time zone. Doing so cansubstantially improve signal to noise ratio. F_(r) _(_) _(i) serves asthe setpoint in feedback control. It can vary from a value causingnegative δFr to a high positive δFr. A high positive number for δFrmeans stronger repulsive interaction with the sample.

FIG. 19 illustrates a procedure 800 of instantaneous force control usedfor Peak Force Tapping (PFT) imaging. In Block 802 an actuatoroscillates the probe or the sample, producing relative motion with anamplitude in the range of 0.1 nm to 3 μm, peak-to-peak. At this point,the tip is relatively far away from the sample, and a baseline andbackground can be determined in Blocks 804 and 806. Once the backgroundis determined, it is also subtracted from the detected deflection inBlock 806 to insure the minimum detectable force is as small aspossible. Block 808 operates to interact the probe with the sample by anengage, as detailed in FIGS. 15 and 16. Once the sample is interactingwith the probe, the deflection data in a period T is sampled anddigitized to analyze Sync Distance (FIG. 18), instantaneous force F_(r)_(_) _(i) and relative force δFr in Block 810. The baseline andbackground can be re-checked according to FIG. 14 at this Block.

Feedback is then used to maintain δFr and F_(r) _(_) _(i) at the presetvalue in Block 812. The XY scanner is also enabled, Block 814, toreposition the probe relative to the sample and eventually generate atopographic image, as well as one or more mechanical images indicativeof, for example, elasticity, adhesion, and energy dissipation.

In FIG. 20 the measurement time resolved curve in FIG. 20A is convertedto real space data in FIG. 20B. More particularly, FIG. 20A is a plot ofthe interaction force as a function of time in one modulation period.FIG. 20B is the interaction force as a function of tip-sample distancein one modulation period. The elastic property of the material can becalculated conventionally by using the upper part of the slope (seesegment DE in FIG. 20B; segments CDE illustrate short range repulsiveinteraction) using, for example, the Oliver-Pharr model, or anothercontact mechanical model. (see, e.g., Oliver W C and Pharr G M 2004Measurement of Hardness and Elastic Modulus by Instrumented Indentation:Advances in Understanding and Refinements to Methodology J. Mater. Res.19 Mar. 20, 2004) The Van der Waals attraction force can be determinedfrom the approaching curve (segment BC in FIGS. 20A and 20B), whilecapillary adhesion, which occurs when the tip departs from the sample,can also be calculated. (see, e.g., “Theoretical Investigation of theDistance Dependence of Capillary and Van der Waals forces in ScanningForce Microscopy”, Stifter et al., Physical Review B, Vol. 62 No. 20,Nov. 15, 2000) By moving the tip in the xy-plane, and repeating thesemeasurements sample properties such as elasticity, Van der Waalsadhesion, capillary adhesion (segment EF corresponds to attraction andcapillary forces) can be imaged for the entire sample surface, or somepart thereof. Furthermore, from the difference of the approaching curveand retrieving (departing) curve, the hardness of the sample can also beimaged.

FIG. 20B represents two types of data, namely direct measurement dataand derived data. Direct measurements data are parameters, such asinteraction force that are determined instantaneously within each cycle.The derived data are calculated data within each interaction cycle fromany part of the curve. Such data can be deformation, which is calculatedby the penetration depth from point C to point D in FIG. 20B. Anotherexample is the dissipation energy defined by the area enclosed in theapproaching curve (BCD) and withdraw curve (EFG). Yet another example isthe adhesion force calculated through the difference between B and F inFIG. 20B. Any of the derived data can be used as the feedback controlparameter. For example, when the deformation is chosen as the feedbackparameter, the control loop in FIG. 1 will produce an image based on aconstant deformation, instead of constant peak force. Any other deriveddata can serve the same purpose in the feedback loop.

One important application of the instantaneous force controlled imagingis in deep trench measurement. When TappingMode™ AFM is used to imagedeep trenches (aspect ratio of about 3:1 or more, with the mostdifficult trenches to image having sub-100 nm width, typically 10 nm-100nm) the strong attractive force at the side walls can cause amplitudechange, resulting in a false measurement of the trench depth. Usingdirect repulsive force as feedback, the feedback only responds toz-change when the tip is in contact with the sample. As a result, theforce controlled feedback can measure deep trenches much more reliablythan TappingMode™ AFM. FIGS. 21A and 21B provide a demonstration of thismeasurement. The measurement uses the same probe and sample at the samesample location. The instantaneous force control feedback loop was ableto give a real trench depth measurement with the tip reaching the trenchbottom (FIG. 21B). TappingMode™ AFM, on the other hand, moved the tipprematurely, yielding a much shallower depth measurement and no trenchbottom was measured (FIG. 21A).

Referring finally to FIGS. 22A/22B and 23A/23B, additional features ofthe present invention are described. In FIGS. 22A and 22B, the AFM isoperated to modulate Z at an amplitude small enough (e.g.,sub-nanometer) to make sure that tip-sample interaction always stays inthe repulsive force zone (Small Amplitude Repulsive Force Mode or SARFMode), i.e., a few nanometers away from surface. This is accomplished byusing either peak-to-peak force difference (F_(a)−F_(b), correspondingto the peak-to-peak Z modulation), or amplitude output of a lock-inamplifier, as feedback. The feedback parameter is proportional to therepulsive force gradient if the amplitude is small enough in which casethe force gradient is linear. In this case, feedback is only sensitiveto short range chemical bonding forces, forces corresponding to atomicresolution. As a result, the present technique is ideal for highresolution imaging.

In FIGS. 23A and 23B, a similar arrangement to that shown in FIGS.22A/22B is shown, but the attractive force portion of the force curve isemployed (Small Amplitude Attractive Force Mode or SAAF Mode). In thiscase, the system modulates Z at an amplitude that is small enough tomake sure tip-sample interaction stays in the attractive force zone allthe time. Again, either simple peak-to-peak force difference(F_(a)−F_(b)), or amplitude output of a lock-in amplifier, can be usedas feedback given that the feedback parameter is proportional to theattractive force gradient if the amplitude is small enough so that theforce gradient is linear. This technique is the least destructive to thesample since the tip does not make contact with the sample. Incomparison to the Small Amplitude Repulsive Force Mode, the feedbackpolarity is inversed.

Advantages

In sum, the benefits of PFT Mode AFM operation are numerous. Given theinherently stable long term force control, drift-free sample imaging canbe achieved along with simultaneous height, stiffness, adhesion,elasticity and plasticity mechanical property measurements atTappingMode™ speeds. Because the technique is not impacted by DC drift(PFT mode creates its own reference every few hundred microseconds),steady operation is not compromised even without an expert operator.This allows the SPM to run for hours, even days (large samples-longtime) without substantially compromising image integrity, particularlyuseful for in-process measurements, like crystal growth and monitoringpolymer phase change, which can take several minutes or hours. Notably,a Peak Force Tapping image can be generated at an operating bandwidthgreater than 2 kHz. Tapping Mode bandwidth is about 1 kHz, primarilybecause cantilever dynamics control speed, e.g., it takes at leastseveral milliseconds to stabilize to return to resonance (greater theamplitude error, the slower). The disclosed embodiments can alsoeliminate phase interpretation problems because it independentlymeasures elasticity, adhesion, energy dissipation, etc. All thesefactors contribute to the phase of cantilever oscillation.

Moreover, PFT Mode is insensitive to cantilever dynamics because thereis no need to wait for complete cantilever ringdown once the probereleases from the sample. This allows for high speed imaging in vacuumand also allows for arbitrary choice among cantilever options. Thisdifference allows mapping over several orders of magnitude ofinteraction force, while repulsive force resolution can be used toproduce artifact free cellular imaging.

The fact that PFT Mode does not have to operate at the resonancefrequency of the probe offers a major advantage when imaging in fluid.Due to various parasitic coupling forces in fluid, cantilever tuning isa key issue in obtaining a fluid image. PFT Mode completely removes theneed to tune the cantilever (baseline averaging, background subtraction,etc.). Furthermore, the range of force control and the ability to use acantilever having a much wider spring constant range (typically, greaterthan 0.3 N/m for TappingMode™ AFM only, while PFT Mode can usecantilevers having spring constants as low as 0.01 N/m) gives imagingcontrol much more room for biological sample imaging.

Again, this is due to the fact that PFT Mode does not depend on theoscillation energy stored in the cantilever to overcome capillaryadhesion forces. Because the technique utilizes an external actuationelement (of the feedback circuit, preferably triggering on peak force),the mechanism to overcome the capillary forces is far more powerful thanin TappingMode™ wherein the static elastic energy of the cantileveritself (fed by the kinetic energy of the oscillating probe) pulls thetip away from the sample in overcoming the capillary forces. As aresult, there is virtually no limitation on the cantilever springconstant to operate stably in presence of a capillary layer. PFT Modetherefore enables stable tapping control operation using a cantileverhaving a spring constant at least as low as 0.01 N/m.

Yet another benefit of the peak force tapping control is the ability touse cantilevers from 0.01 N/m to 1000 N/m in one mode of AFM operation.It enables high resolution mechanical property mapping of the broadestrange of materials on a single instrument from 10 kPa to 100 GPa inelastic modulus.

In addition, given essentially instantaneous force feedback, tipcrashing is virtually eliminated. Also, because the deflection ishydrodynamically corrected, no tuning is typically required, andtherefore fast, ready setup by virtually any user can be accomplished.

When compared to existing modes of AFM operation, the low force highspeed imaging provided by PFT Mode in combination with the low averagetracking force and the virtual elimination of lateral forces on the tip,provide a significant advance in high speed imaging over a wide varietyof samples. For example, single molecule elasticity can be measured, aswell as narrow DNA samples in fluid (e.g., 2 nm wide DNA). Bycomparison, when imaging DNA in fluid, TappingMode™ AFM has at least a 2nm lower resolution. Moreover, measuring DNA stiffness in fluid ischallenging with TappingMode™ AFM because it does not have propertyquantification capacity, it primarily is only able to provide relativemechanical property measurements (for example, by looking at contrast inphase images). With the present technique, property measuring down tothe molecular level can be achieved.

In the end, PFT Mode can acquire data as good as or better (a resolution[e.g., less than a 100 nm, and more preferably less than about 1 nmlaterally], etc.) than that acquired in TappingMode™ AFM withoutdamaging the tip and/or the sample. The technique provides significantspeed improvement over other known force feedback techniques and does sowithout requiring the use of a small lever. In fact, a rather largelever (>60 μm long) can be operated at sub-resonance in PFT Mode so thatthe lever response has a bandwidth far beyond that achievable when usinga so-called small cantilever (>10 kHz).

Of course, an additional benefit of the present preferred embodiments isthat a force curve is generated with every pixel so that the imageprovides information beyond a typically TappingMode™ AFM image. Withevery pixel, the user can obtain quantitative information regardingstiffness, adhesion, elasticity, plasticity, etc. And again, becausebaseline tip-sample separation is re-zeroed with every pixel, drift isminimized so that a large improvement in productivity and imagereliability is realized.

In review, the present PFT Mode provides very low force imaging toprovide very high resolution using real time property mapping (i.e.,instantaneous force control). The force control is inherently stable(essentially drift free), over a term sufficiently long to image asample with minimal or no user intervention. The system allows faster,simpler set-up because no tuning is required (baseline averaging andhydrodynamic background correction). Moreover, precise control overforce basically eliminates tip crash, while the technique/system alsoessentially eliminates lateral force on the sample surface. The systemis also insensitive to cantilever dynamics by not having to wait forprobe ringdown before interacting the probe with the sample once itreleases from the sample. And, as discussed, a wide range of cantileversare available to the user to obtain simultaneous measurements of height,stiffness, adhesion, elasticity and plasticity at TappingMode™ AFMspeeds (>2 kHz). The present SPM can image samples such as 2 nm wide DNAin fluid with these characteristics, as well make improved mechanicalproperty measurements such as single molecule elasticity.

Although the best mode contemplated by the inventors of carrying out thepresent invention is disclosed above, practice of the above invention isnot limited thereto. It will be manifest that various additions,modifications and rearrangements of the features of the presentinvention may be made without deviating from the spirit and the scope ofthe underlying inventive concept.

The invention claimed is:
 1. A method of operating a scanning probemicroscope (SPM) comprising: interacting a tip of a probe of the SPMwith a sample; then terminating the interaction, resulting in a decayingprobe oscillation; repeating the interaction before ringdown of thedecaying probe oscillation is substantially complete; and detectingmotion of the probe during the interaction step; determining aninstantaneous force on the tip based on the detecting step; using theinstantaneous force as a feedback control parameter to operate the SPM;and further comprising determining a synchronization distance and usingthe synchronization distance to determine the instantaneous force. 2.The method of claim 1, wherein the synchronization distance isdetermined using one of A) measuring the phase delay between thedetected motion and a drive signal of the oscillating step, and B)measuring a distance between initiating a period of the drive signal andan instant of interaction between the probe and the sample.
 3. Themethod of claim 1, wherein the synchronization distance is determinedusing a window.
 4. The method of claim 1, wherein the determining stepincludes subtracting that portion of the detected motion caused byparasitic forces from the detected motion.
 5. The method of claim 4,wherein a minimum controllable force upon performing the subtractionstep is at least about an order of magnitude less than a minimumcontrollable force without perforating the subtraction step.
 6. Themethod of claim 5, wherein the minimum controllable force is about 1 pNwhen the cantilever has a length equal to about 100 microns and a springconstant of about 0.01 N/m.
 7. The method of claim 4, wherein theparasitic forces are caused by a hydrodynamic background.